What is the integral from 0 to 4 of x^2-7x+12 ?

The integral from 0 to 4 of x^2-7x+12 is 40/3

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integral from 0 to 4 of x^2-7x+12

\int_{0}^{4} x^{2} - 7 x + 12 d x

\frac{40}{3}

Decimal

13.33333 \dots

Solution steps

\int_{0}^{4} x^{2} - 7 x + 12 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{4} x^{2} d x - \int_{0}^{4} 7 x d x + \int_{0}^{4} 12 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 7 x d x = 56

\int_{0}^{4} 12 d x = 48

= \frac{64}{3} - 56 + 48

Simplify

\frac{64}{3} - 56 + 48 : \frac{40}{3}

= \frac{40}{3}

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What is the integral from 0 to 4 of x^2-7x+12 ?
The integral from 0 to 4 of x^2-7x+12 is 40/3